Diffraction of rotated measures

Abstract

Consider a translation-bounded measure on the line. We can rotate the measure, distributing the mass proportionally to the area, to create a two-dimensional rotationally invariant translation-bounded measure. We show that the diffraction of the two-dimensional object is the normalised rotation of the diffraction of the original measure. We discuss some examples and generalisation beyond $d=2$.

arXiv comment24 pages, 1 figure